What do you think about:
Can I expect the OM-d to deliver as good photo quality as the D7000?

If you are shooting JPEGs, possibly yes. I would not expect the same quality in RAW.

What drawbacks can I expect with the EVF?

For me the main difference is that while OVF is showing the input (real world), the EVF is showing the output (real world with applied settings and limited by electronics quality). Means that you will miss the real dynamics, colours and white balance, but get a better control over the output in the moment of shooting. The preference is a matter of personal taste.

How is the Af for moving targets compared to D7000?

Do not expect the same performance as D7000. Not even close.

I would like to have a faster normal zoom lens - suggestions

As far as I know, such lens (f/2.8 through the range) is expected to come from Panny. Be prepared for premium price.
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